Instantons and Khovanov skein homology on
Yi Xie
Peking University, Beijing, P. R. ChinaBoyu Zhang
Princeton University, College Park, USA
![Instantons and Khovanov skein homology on $I\times T^{2}$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-qt.png&w=3840&q=90)
Abstract
Asaeda, Przytycki, and Sikora (2004) defined a generalization of Khovanov homology for links in -bundles over compact surfaces. We prove that, for a link , the Asaeda–Przytycki–Sikora homology of has rank with -coefficients if and only if is isotopic to an embedded knot in . We also prove that Asaeda–Przytycki–Sikora homology detects the unlink and torus links in .
Cite this article
Yi Xie, Boyu Zhang, Instantons and Khovanov skein homology on . Quantum Topol. (2024), published online first
DOI 10.4171/QT/184